The invention is based on a device for measuring the mass of a flowing medium as described by the preamble to the main claim. A device for measuring the mass of a flowing medium is already known in which a hot wire is used as a temperature-dependent resistor, which wire is tautly fastened at a plurality of fastening points in a sensor ring and extends perpendicularly to the flow direction of the medium. It has been demonstrated that finely-grained, dry silicate dust, to which the sensor may be exposed during trips in dusty regions, can form an undesirable coating on the hot wire, restricting the measurement precision of the wire and perhaps even causing the destruction of the wire. The prior art has attempted to cope with this phenomena, but even the known process of burning off deposits by heating the wire to red-hot temperatures does not bring about a satisfactory restoration of the wire's measurement precision; in fact, it may worsen the situation, because the dust particles can become firmly sintered to the wire.